Question: $A$ $B$ $C$ If: $ AC = 64$, $ AB = 7x + 8$, and $ BC = 3x + 6$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 8} + {3x + 6} = {64}$ Combine like terms: $ 10x + 14 = {64}$ Subtract $14$ from both sides: $ 10x = 50$ Divide both sides by $10$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 3({5}) + 6$ Simplify: $ {BC = 15 + 6}$ Simplify to find ${BC}$ : $ {BC = 21}$